5 problems

Locally conformally symplectic non-squeezing conjecture. If $R\geq 1$, there is no compactly supported Hamiltonian lcs map

Let $1<k<m$, let $\varphi\in\operatorname{Symp}(\mathbb R^{2m})$, and let $P_{\mathbb R^{2k}}:\mathbb R^{2m}\to\mathbb R^{2k}$ be projection onto the first $2k$ coordinates. Assume…

Let $B^{2n}\subset\mathbb{R}^{2n}$ be the symplectic ball, let $V\subset\mathbb{R}^{2n}$ be a symplectic $2k$-dimensional subspace with $1<k<n$, and let $P_V$ be the symplectic lin…

Coarse non-squeezing conjecture. Coarse non-squeezing at large scale holds for prequantizations $M\times S^1$ of sufficiently stabilized Liouville manifolds $M$.

Let $V$ be a $2k$-dimensional symplectic subspace of $(\mathbb{R}^{2n},\omega_0)$ with $1<k<n$, let $P$ be the symplectic projector onto $V$, and let $B$ be the unit ball in…